Basis Expansion/Examples/3 Quarters in Decimal
Jump to navigation
Jump to search
Example of Basis Expansion
The fraction $\dfrac 3 4$ has a basis expansion in decimal (base $10$) notation as:
- $0 \cdotp 75$
Proof
| \(\ds 0 \cdotp 75\) | \(=\) | \(\ds 7 \times 10^{-1} + 5 \times \times 10^{-2}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {70 + 5} {10^2}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {75} {100}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {3 \times 25} {4 \times 25}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 3 4\) |
$\blacksquare$
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): expansion: 2.